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Scheduling - Beginner-Intermediate Level: monthly schedule BEGINNER-INTERMEDIATE

Ready to master scheduling? This benchmark test features 20 beginner-intermediate-level challenges. Worksheet 12 of 30 sharpens your monthly schedule skills. Master appointment logic, calendar scheduling, shift planning through guided practice. Perfect for developing test preparation.

📝 Worksheet 12 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Beginner-intermediate level

What you'll learn in this worksheet:
Your progress through Scheduling
Worksheet 12 of 30 (40% complete)

Question 1

Project scheduling with two objectives: minimize time and minimize cost. - Schedule A: 100 days, $50K - Schedule B: 120 days, $40K - Schedule C: 90 days, $60K - Schedule D: 110 days, $45K - Schedule E: 95 days, $55K Which schedules are on the Pareto frontier (not dominated in both objectives)?
Step-by-step solution:

1. Pareto dominance: Schedule X dominates Y if X is better in at least one objective and not worse in others
2. Pareto frontier schedules: Schedule A, Schedule B, Schedule C, Schedule D, Schedule E

Answer: Schedule A, Schedule B, Schedule C, Schedule D, Schedule E
pareto, multi-objective, trade-off, advanced, optimization

Question 2

An airline crew has the following flights: - Flight 101: 08:00 → 10:00 - Flight 102: 10:30 → 12:30 - Flight 103: 13:00 → 15:00 - Flight 104: 15:30 → 17:30 - Flight 105: 18:00 → 20:00 Crew duty time limit is 8 hours. Minimum connection time between flights is 30 minutes. What is the maximum number of flights a crew can operate in a single duty period?
Step-by-step solution:

1. Convert all times to minutes for easier calculation:
- Flight 101: Departs at 8:00, Arrives at 10:00
- Flight 102: Departs at 10:30, Arrives at 12:30
- Flight 103: Departs at 13:00, Arrives at 15:00
- Flight 104: Departs at 15:30, Arrives at 17:30
- Flight 105: Departs at 18:00, Arrives at 20:00

2. Duty time limit: 480 minutes (8 hours)
3. Minimum connection time: 30 minutes

4. Find optimal sequence of flights:
Best sequence found: Flight 103 → Flight 104 → Flight 105
- Take Flight 103: Departs at 13:00
- Connection time: 30 minutes
- Take Flight 104: Departs at 15:30
- Connection time: 30 minutes
- Take Flight 105: Departs at 18:00

Total duty time: 420 minutes (7 hours, 0 minutes)

5. Maximum flights possible: 3

Answer: 3 flights

✓ Duty time check: 7h 0m ≤ 8h (PASSED)
airline, crew, flight, aviation, rostering

Question 3

Trains and their scheduled times (arrival, departure): - Train 1: 2:00 → 6:00 - Train 2: 7:00 → 11:00 - Train 3: 7:00 → 10:00 - Train 4: 16:00 → 18:00 - Train 5: 18:00 → 20:00 What is the minimum number of platforms needed to avoid conflicts?
Step-by-step solution:

1. Sort trains by arrival time
2. Greedy platform allocation
3. Maximum overlapping trains: 2

Answer: 2 platforms
railway, platform, track, transportation, conflict

Question 4

A machine can process up to 6 jobs simultaneously as a batch. Each batch takes 40 minutes. If 15 jobs need to be processed, what is the minimum total time required?
Step-by-step solution:

1. Jobs per batch: 6
2. Number of batches: ⌈15 ÷ 6⌉ = 3
3. Total time: 3 × 40 = 120 minutes

Answer: 120 minutes
batch, parallel-machines, capacity, manufacturing, optimization

Question 5

Round Robin scheduling with time quantum = 3: - P1: Burst time 11 - P2: Burst time 12 - P3: Burst time 14 - P4: Burst time 13 What is the average completion time?
Step-by-step solution:

1. Round Robin simulation:
2. Completion times:
- P1: 38
- P2: 41
- P3: 49
- P4: 50

3. Average: 178 ÷ 4 = 44.5

Answer: 44.5
preemptive, interruptible, round-robin, OS, computer-science

Question 6

Four employees need to be scheduled for three shifts over three days. The constraints are: - Each employee works exactly one shift per day - No employee works the same shift two days in a row - Alice works Morning shift on Monday - Bob cannot work Night shift - Charlie works Evening shift on Tuesday Who works the Evening shift on Wednesday?
Step-by-step solution:

Table Method with Constraint Elimination:
1. Create a 3D table: Days x Shifts x Employees

2. Apply direct constraints:
- Monday Morning: Alice (fixed)
- Tuesday Evening: Charlie (fixed)
- Bob: Never Night shift (all days)

3. Apply rotation constraint:
- Alice (Morning Mon) cannot be Morning Tue
- Charlie (Evening Tue) cannot be Evening Wed

4. Fill Monday:
- Morning: Alice
- Evening: Charlie (can work evening)
- Night: Diana (Bob can't do night)

5. Fill Tuesday:
- Morning: Bob (Alice can't repeat, Charlie is evening)
- Evening: Charlie (fixed)
- Night: Diana (Bob can't)

6. Fill Wednesday:
- Charlie can't be Evening (was Evening Tue)
- Alice can be Evening (was Morning Mon, okay to shift)
- Answer: Alice works Evening on Wednesday

Key Strategy: Apply fixed constraints first, then use rotation rules to eliminate impossible assignments systematically.
shift-rotation, multi-person, constraints, professional

Question 7

Five subjects are scheduled on five different days of the week (Monday to Friday), one subject per day. The following information is given: - Chemistry is scheduled on Wednesday - Physics is scheduled immediately after Biology - There are exactly two classes between Mathematics and English - Biology is not on Monday On which day is Physics scheduled?
Step-by-step solution:

Table Method:
1. Create a timeline for Monday to Friday
2. Apply direct constraints:
- Chemistry is on Wednesday (fixed)
- Biology is not on Monday
3. Apply consecutive constraint:
- Physics immediately follows Biology
- Possible pairs: (Tue-Wed), (Wed-Thu), (Thu-Fri)
- Since Wednesday is occupied, options are (Tue-Wed) or (Thu-Fri)
4. Apply gap constraint:
- Two classes between Mathematics and English
5. Final schedule:
- Monday: Mathematics
- Tuesday: English
- Wednesday: Chemistry
- Thursday: Biology
- Friday: Physics

Answer: Physics is scheduled on Friday

Key Strategy: Fix direct constraints first, then work with consecutive and gap constraints.
weekly, academic, day-based, constraints

Question 8

Five patients need appointments. Their preferences are: - Patient A: Dr. Patel at 10:00 AM - Patient B: Dr. Kumar at 10:00 AM - Patient C: Dr. Patel at 10:30 AM - Patient D: Dr. Shah at 10:00 AM - Patient E: Dr. Patel at 11:00 AM Each doctor can see one patient per 30-minute slot. If all preferences are honored, how many patients need to be rescheduled?
Step-by-step solution:

Conflict Detection Method:
1. Create doctor-time matrix:
Doctor | 10:00 | 10:30 | 11:00 | 11:30
------------|-------|-------|-------|-------
Dr. Patel | A | C | E | ---
Dr. Kumar | B | --- | --- | ---
Dr. Shah | D | --- | --- | ---

2. Check for conflicts:
- Dr. Patel at 10:00: Only Patient A (No conflict)
- Dr. Patel at 10:30: Only Patient C (No conflict)
- Dr. Patel at 11:00: Only Patient E (No conflict)
- Dr. Kumar at 10:00: Only Patient B (No conflict)
- Dr. Shah at 10:00: Only Patient D (No conflict)

3. Verification:
- No doctor has multiple patients in same slot
- All preferences can be honored

Answer: 0 patients need rescheduling

Key Strategy: Map all appointments to a doctor-time grid and identify slots where multiple patients request the same doctor.
appointment, conflict-resolution, multi-person

Question 9

A clinic operates for 4 hours with 30-minute appointment slots. If 8 patients need appointments, how many can be accommodated?
Step-by-step solution:

1. Total slots available: (4 × 60) ÷ 30 = 8
2. Patients: 8
3. All patients can be scheduled

Answer: All 8 patients can be scheduled
clinic, appointment, doctor, healthcare, wait-time

Question 10

Given these scheduling constraints: - Task A must be before Task B - Task D must be after Task B - Task C must be immediately after Task A Is a valid schedule possible?
Step-by-step solution:

1. Check for cycles: No circular dependencies
2. Check immediate constraints: Can be satisfied
3. Conclusion: Yes, a valid schedule exists

Answer: Yes, a valid schedule exists
feasibility, satisfiability, constraint-check, logic, verification

Question 11

Events need to be scheduled in rooms. Their time intervals are: - Event A: 12:00 to 14:00 - Event B: 3:00 to 6:00 - Event C: 16:00 to 19:00 - Event D: 18:00 to 24:00 - Event E: 3:00 to 10:00 - Event F: 15:00 to 21:00 - Event G: 10:00 to 11:00 - Event H: 10:00 to 16:00 What is the minimum number of rooms needed to schedule all events without overlap?
Step-by-step solution (Interval Graph):

1. Plot intervals on timeline:
Event A: ██ from 12 to 14
Event B: ███ from 3 to 6
Event C: ███ from 16 to 19
Event D: ██████ from 18 to 24
Event E: ███████ from 3 to 10
Event F: ██████ from 15 to 21
Event G: █ from 10 to 11
Event H: ██████ from 10 to 16

2. Find maximum overlap:
Maximum 3 events overlap at once

Answer: 3 rooms needed
interval, overlap, room-allocation, graph-theory, optimization

Question 12

Project scheduling with two objectives: minimize time and minimize cost. - Schedule A: 100 days, $50K - Schedule B: 120 days, $40K - Schedule C: 90 days, $60K - Schedule D: 110 days, $45K - Schedule E: 95 days, $55K Which schedules are on the Pareto frontier (not dominated in both objectives)?
Step-by-step solution:

1. Pareto dominance: Schedule X dominates Y if X is better in at least one objective and not worse in others
2. Pareto frontier schedules: Schedule A, Schedule B, Schedule C, Schedule D, Schedule E

Answer: Schedule A, Schedule B, Schedule C, Schedule D, Schedule E
pareto, multi-objective, trade-off, advanced, optimization

Question 13

**Data Sufficiency Question** A project has 4 phases: Planning, Design, Development, Testing. **Question:** On which day does Development start? **Statement (1):** Testing starts exactly 5 days after Design ends. **Statement (2):** Planning takes 3 days and ends before Design starts. **Options:** A. Statement (1) ALONE is sufficient, but statement (2) alone is NOT sufficient B. Statement (2) ALONE is sufficient, but statement (1) alone is NOT sufficient C. BOTH statements TOGETHER are sufficient, but NEITHER alone is sufficient D. EACH statement ALONE is sufficient E. Statements (1) and (2) TOGETHER are NOT sufficient
Data Sufficiency Reasoning:

Step 1 - Analyze Statement (1) alone: Testing starts exactly 5 days after Design ends.
This gives partial information but not enough to determine the answer uniquely.

Step 2 - Analyze Statement (2) alone: Planning takes 3 days and ends before Design starts.
This also gives partial information insufficient by itself.

Step 3 - Combine statements:
Together, they provide enough constraints to solve uniquely.

Conclusion: Both statements together are still insufficient.

Key Strategy: Test each statement independently first, then combine only if neither alone works.
data-sufficiency, GMAT, CAT, reasoning, test-prep

Question 14

A project consists of the following tasks: - Task A (Requirements Analysis): 2 days, Depends on: None - Task B (Design): 3 days, Depends on: A - Task C (Database Setup): 2 days, Depends on: A - Task D (Development): 5 days, Depends on: B, C - Task E (Testing): 3 days, Depends on: D What is the minimum number of days required to complete the entire project?
Step-by-step solution:

Critical Path Method (CPM):
1. Identify dependencies and calculate earliest start times:
- Task A: Starts on Day 0, Duration 2 days
Finishes on Day 2
- Task B: Starts on Day 2, Duration 3 days
Finishes on Day 5
- Task C: Starts on Day 2, Duration 2 days
Finishes on Day 4
- Task D: Starts on Day 5, Duration 5 days
Finishes on Day 10
- Task E: Starts on Day 10, Duration 3 days
Finishes on Day 13

2. Task timeline:
Task A: Days 0-2
Task B: Days 2-5 (after A)
Task C: Days 2-4 (after A)
Task D: Days 5-10 (after B and C)
Task E: Days 10-13 (after D)

3. Critical path: A -> B -> D -> E (or A -> C -> D -> E)
4. Total project duration: 13 days

Key Strategy: Calculate earliest start time for each task based on predecessor completion times; the longest path determines total duration.
project-management, dependencies, critical-path, professional

Question 15

Project scheduling with two objectives: minimize time and minimize cost. - Schedule A: 100 days, $50K - Schedule B: 120 days, $40K - Schedule C: 90 days, $60K - Schedule D: 110 days, $45K - Schedule E: 95 days, $55K Which schedules are on the Pareto frontier (not dominated in both objectives)?
Step-by-step solution:

1. Pareto dominance: Schedule X dominates Y if X is better in at least one objective and not worse in others
2. Pareto frontier schedules: Schedule A, Schedule B, Schedule C, Schedule D, Schedule E

Answer: Schedule A, Schedule B, Schedule C, Schedule D, Schedule E
pareto, multi-objective, trade-off, advanced, optimization

Question 16

A factory has 3 production lines: Line 1, Line 2, Line 3. Three products require the following operations: **Product X:** - Cut: 30 min on Line 3 - Assemble: 45 min on Line 2 - Package: 15 min on Line 1 **Product Y:** - Cut: 20 min on Line 1 - Assemble: 60 min on Line 2 - Package: 20 min on Line 2 **Product Z:** - Cut: 40 min on Line 1 - Assemble: 30 min on Line 2 - Package: 25 min on Line 2 All products must be completed (all 3 operations each). Multiple operations can run in parallel on different lines. Which production line is the bottleneck, and what is its total load (in minutes)?
Step-by-step solution (Bottleneck Analysis):

1. Calculate total load per production line:
- Line 1: 75 minutes
- Line 2: 180 minutes
- Line 3: 30 minutes

2. Identify bottleneck: The line with maximum load = Line 2
3. Bottleneck load: 180 minutes

Answer: Line 2 (180 minutes)

Key Strategy: The bottleneck determines maximum throughput; optimize the bottleneck first for overall efficiency.
nested, bottleneck, resource-allocation, multi-line, factory

Question 17

Real-time tasks with Rate Monotonic Scheduling (shorter period = higher priority): - Task A: Execution 16, Period 50 - Task B: Execution 15, Period 50 - Task C: Execution 11, Period 40 - Task D: Execution 2, Period 20 Is the task set schedulable under RM?
Step-by-step solution:

1. Calculate utilization:
- Task A: 16/50 = 0.320
- Task B: 15/50 = 0.300
- Task C: 11/40 = 0.275
- Task D: 2/20 = 0.100
Total U = 0.995
2. RM schedulability bound for 4 tasks: 0.757
3. Conclusion: Utilization 0.995 > 0.757 (RM bound)

Answer: May not be schedulable
real-time, deadline, rate-monotonic, embedded, OS

Question 18

A hospital needs to schedule 5 staff for 7 days (Saturday, Friday, Wednesday...). Each day has 3 shifts: Morning, Evening, Night. Undesirable shifts (higher weight = more undesirable): - Weekend Night: weight 3 - Weekend Evening: weight 2 - Any Night: weight 1 After creating a fair schedule, what is the fairness gap (difference between max and min undesirable weights assigned to any staff)?
Step-by-step solution (Fairness Scheduling):

1. Total shifts to assign:
- 7 days × 3 shifts = 21 shifts
2. Shifts per person: 21 ÷ 5 = 4 with 1 extra shifts
3. Undesirable weight distribution:
- Alice: 4 points
- Bob: 2 points
- David: 1 points
- Emma: 4 points
- Frank: 4 points

4. Fairness gap: 4 - 1 = 3

Key Strategy: Fair scheduling aims to minimize the maximum difference in undesirable shift assignments across all staff.
fairness, shift-scheduling, workforce, equity, human-resources

Question 19

Eight people attend seminars in four different months (January, March, May, July) on two dates (5th and 15th). Two people attend per month. The constraints are: - Q attends in March - P attends on the 15th - Exactly two people attend between W and T - V attends in the same month as U In which month does W attend?
Step-by-step solution:

Timeline Grid Method:
1. Create month-date grid:
Jan 5 | Jan 15 | Mar 5 | Mar 15 | May 5 | May 15 | Jul 5 | Jul 15

2. Apply constraints:
- Q in March (Mar 5 or Mar 15)
- P on 15th (any month, date 15)
- Two people between W and T
(If W at position 1, T at position 4)
- V and U in same month

3. Systematic placement:
- Place Q at Mar 5 (satisfies March constraint)
- Place P at Mar 15 (satisfies 15th constraint)
- For 'two between' constraint: If W at Jan 5, T at Mar 15
- V and U together: May 5 & May 15

4. Verification:
All constraints satisfied with W in March

Key Strategy: Use grid to visualize all slots, apply direct constraints first, then deduce positions using gap constraints.
month-based, date-based, gap-constraints, banking-exams

Question 20

A student has 7 days to prepare for three exams: Computer Science, Mathematics, Physics. The required preparation days are: - Computer Science: 1 days - Mathematics: 3 days - Physics: 2 days If the student follows the optimal schedule starting today, on which day will the last exam be?
Step-by-step solution:

Timeline Planning Method:
1. Calculate total preparation time needed:
- Computer Science: 1 days
- Mathematics: 3 days
- Physics: 2 days
- Total: 6 days

2. Available days: 7 days
3. Extra buffer days: 1 days
4. Optimal schedule:
- Days 1-1: Prepare for Computer Science
- Day 2: Computer Science exam
- Days 3-5: Prepare for Mathematics
- Day 6: Mathematics exam
- Days 7-8: Prepare for Physics
- Day 9: Physics exam

Answer: The last exam will be on Day 7

Key Strategy: Schedule exams immediately after preparation period ends, accounting for all required prep days.
academic, deadline, preparation, timeline
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